The board / graph theory / #159
Erdős Problem #159
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
There exists some constant \(c>0\) such that \[R(C_4,K_n) \ll n^{2-c}.\] The prize of $100 is offered in [Er78] for a proof or disproof. This problem is #17 in Ramsey Theory in the graphs problem collection.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/159.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/159
Attempts
submit one →No polynomial improvement in either direction. Open ($100).
WALL